The minimum/maximum value of the function y = a(x − 2)(x − 1) occurs at x = d, what is the value of d?
Answer:
[tex]d=\frac{3}{2}=1.5[/tex]
Step-by-step explanation:
We have the function:
[tex]y=a(x-2)(x-1)[/tex]
And we want to find x=d for which the minimum/maximum value will occur.
Notice that our function is a quadratic in factored form.
Remember that the minimum/maximum value always occurs at the vertex point.
And remember that the x-coordinate of the vertex is the axis of symmetry.
Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.
Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.
Our factors are (x-2) and (x-1).
Therefore, our roots/zeros are x=1, 2.
So, the average of them are:
[tex]d=\frac{1+2}{2}=3/2=1.5[/tex]
Therefore, regardless of the value of a, the minimum/maximum value will occur at x=d=1.5.
Alternative Method:
Of course, we can also expand to confirm our answer. So:
[tex]y=a(x^2-2x-x+2)\\y=a(x^2-3x+2)\\y=ax^2-3ax+2a[/tex]
The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.
And the formula for the vertex is:
[tex]x=-\frac{b}{2a}[/tex]
So, we will substitute -3a for b and a for a. This yields:
[tex]x=-\frac{-3a}{2a}=\frac{3}{2}=1.5[/tex]
Confirming our answer.
An investor invested a total of $2,800 in two mutual funds. One fund earned a 9% profit while the other earned a 4% profit. If the investor's total profit was 5197 how much was invested in each mutual fund?
The amount invested in the mutual fund that earned 9% was $
help pls do in 5 mins points and brainly offerd
In a certain country, the heights and depths of a road are measured in relation to sea level. Sea level has a value of 0. The lowest point of the country lies at –7 feet. The highest point of the country lies at +112 feet. Which of the following statements best describes the lowest and the highest points?
The lowest point is 7 feet above sea level, and the highest point is 112 feet below the lowest point.
The lowest point is 7 feet below sea level, and the highest point is 112 feet above the lowest point.
The lowest point is 7 feet above sea level, and the highest point is 112 feet below sea level.
The lowest point is 7 feet below sea level, and the highest point is 112 feet above sea level.
Answer: D.The lowest point is 7 feet below sea level, and the highest point is 112 feet above sea level.
Step-by-step explanation:
Answer:
joogy joogy
Step-by-step explanation:
0.3:2=d:8 find d
i'll mark brainliest if you are correct.
Answer:
1.2
Step-by-step explanation:
0.3/2 = d/8
multiply 0.3 by 4 which is 1.2 because 2 * 4 is 8
Please answer C: <3!
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
What does this mean how much answers do I need
If you want to talk to someone 1 on 1 you need to answer questions
either that or you can’t ask questions if you haven’t answered any questions
For each picture identify each transversal and identify each given pair of angles as alternate interior/exterior, corresponding, same side interior/exterior or neither: ∠2 and ∠4, ∠1 and ∠8, ∠4 and ∠5, ∠1 and ∠5, ∠3 and ∠5
Answer: "interior, congruent, parallel, exterior, supplementary,
Step-by-step explanation:
Which term best describes the graph of y = x – 1?
increasing
decreasing
constant
positive
Since the slope is a positive slope, hence the term that best describes the graph of y = x – 1 is increasing
The standard equation of a line in slope-intercept form is expressed as:
y = mx + b
where:
m is the slope of the lineb is the y-intercept of the lineThe nature of the graph is determined by the slope value.
If the slope is positive, the graph is increasing while if the slope is negative, the graph is decreasing.
Given the function y = x - 1, compared with the general equation;
mx = 1x
m = 1
Since the slope is a positive slope, hence the term that best describes the graph of y = x – 1 is increasing
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Help with this please. (Math)
Answer:
Step-by-step explanation:
$4,000 × 0.06 × 5 = $1,200
If sally is 5 feet and 2 inches . how many inches is she?
Answer:
62 inchs
Step-by-step explanation:
5Feet= 60 inchs + 2 is 62
Answer: she is 62 inches
Step-by-step explanation:
You would figure out how many inches in a foot which is 12 then times it by 5 then add 2
What is y?
-74 × y =40
Answer:
y= −20/37
Step-by-step explanation:
Find the x-intercept of the graph of the equation =−.+y equals negative , 2.65 , x plus 25.
What does the x-intercept mean in terms of the situation?
Answer:
Ok so we can see for every 2 cups of medium coffee, the balance goes down 5.30$. So that means that for every coffee, her balance goes down 2.65$. Solving for the x-intercept means how many medium coffees can I get until my balance is 0. First, we have to find the y-int so it's easy. The slope is -2.65 because for every medium coffee, her balance goes down 2.65$. So we have y=-2.65x+b. Plugging in any point, I choose (4,14.40), we get 14.4 = -2.65 × 4 +b. Solving for b we get 25 for the y intercept, meaning the equation is y = -2.65x + 25 . To find the x intercept, we set y=0. So we have 0 = -2.65x+25. Solving for x we get approx. 9.4. We can't have decimals so we round down to 9. So the x int is ≈ 9.4 meaning we can only buy 9 coffee and have a little extra. But, if the problem said how many more coffees can she get, then here is how we do it. Since she already got 4 coffees, and the max is 9, we do 9-4 and we get 5, so she can buy 5 coffeed more.
Step-by-step explanation:
PLZ HELP ME
What linear equation is represented by the table?
y=2x
y=4x
y=2x-3
y=4x -3
PLS HELP ASAP PLS GIVE A GOOD EXPLANATION
Answer:
-444
Step-by-step explanation:
-761 - (-317) = ?
? = -444
Also, Why do you have hw on the weekend fran?
Please help me answer this
Answer:
The answer is c
Step-by-step explanation:
Terri buys five and seven eighths ounces of chocolate chips. She uses four and four sixths ounces in a recipe. How many ounces of chocolate chips does she have left?
one and ten forty eighths ounces
one and three fourteenths ounces
two and ten forty eighths ounces
two and three fourteenths ounces
Answer:
Two and ten forty eighths ounces....
Hope this helps :D
Answer:
maybe d??????????
Step-by-step explanation:
please mark brain
Write an EQUATION for the nth term of each arithmetic sequence
15,13,11,9,...
Match the fractions with equivalent percentages.
arrowBoth
arrowBoth
arrowBoth
arrowBoth
Answer:
C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Elevator 1 in a building moved from ground position to a final position of +17 feet. Elevator 2 in the same building moved from ground to a final position of –22 feet. Which statement best describes the final positions of these two elevators? (1 point)
Elevator 1 is 17 feet below ground level, and elevator 2 is 22 feet above ground level.
Elevator 1 is 17 feet above ground level, and elevator 2 is 22 feet below ground level.
Elevator 1 is 17 feet above ground level, and Elevator 2 is 22 feet below the position of Elevator 1.
Elevator 1 is 17 feet below ground level, and Elevator 2 is 22 feet above the position of Elevator 1.
Answer:
B
Step-by-step explanation:
17 is positive meaning above while 22 is negative meaning below
hope this helps :3
if it did pls mark brainliest
Answer:
b
Step-by-step explanation:
A convenience store sells two brands of orange juice. Brand a contains 8 fluid ounces and cost $1.58. Brand B contains 12 fluid ounces and cost $1.98. Which brand cost less per ounces
There are 8 sixth-grade classes and 195 sixth grade students at Edison Middle
school. The equation 8s = 195 can be used to determine s, the mean number of students per class. Based on the solution s = 24.375, which of the following statements could be true?
A. There are 5 sixth-grade classes with 24 students each and 3 sixth-grade classes with 25 students each.
B. There are 7 sixth-grade classes with 24 students each and 1 sixth grade class with 25
students.
C. There are 8 sixth-grade classes with 25 students each.
D. There are 8 sixth-grade classes with 24 students each
Answer:
D
Step-by-step explanation:
You just have to round the decimal
2 movie tickets and 1 popcorn cost $29. 4 movie tickets and 4 popcorns cost $68. And 1 movie ticket cost $12. Using the same information from the infomation above, how much would 3 movie tickets and 5 popcorns cost?
A.$52
B.$58
C.$61
D.$67
Answer:
C - $61
Step-by-step explanation:
I did all the math on my paper tell me if you need evidence
Answer:
61
Step-by-step explanation:
1 movie ticket= $12
1 popcorn= $5
x: 39, 40, 41, 42,
y: 36, 29, 22, 15
What is the slope of the line that contains these points?
Answer:
it is -7/1 or -7
Step-by-step explanation:
Water boils at 100 degrees celsius or 212 degrees fahrenheit. Water freezes at 0 degrees celsius or 32 degrees fahrenheit. If the weather forecaster says it will be 25 degrees celsius today. write and solve a linear equation to find what fahrenheit temperature this is.
Answer:
given with two conditions: after 0 degrees Celsius, this is equal to 32 degrees Fahrenheit and after at 100 degrees Celsius, this is equal to 212 degrees Fahrenheit . We translate these into points, we have (0,32) and (100, 212). we get the slope of the points ((212-32)/100) or 9/5. we plug to the equation y-y1 = m (x-x1) where m is equal to 9/5. y-32 = 9/5 (x-0). Simplifying, we get y -32 = 9x/5 or equal to y = 9/5 x + 32 where x is degrees Celsius and y is degrees Fahrenheit.
hope this helps
The given temperature is required in Fahrenheit.
The required temperature is 77 degrees Fahrenheit.
Let the x axis denote Celsius
and y axis denote Fahrenheit
The ordered pairs are [tex](100,212)[/tex] and [tex](0,32)[/tex]
The equation of the line will be
[tex]y-212=\dfrac{32-212}{0-100}(x-100)\\\Rightarrow y-212=1.8(x-100)\\\Rightarrow y-212=1.8x-180\\\Rightarrow y=1.8x+32[/tex]
The temperature is 25 degrees Celsius so [tex]x=25[/tex]
[tex]y=1.8\times 25+32\\\Rightarrow y=77[/tex]
The required temperature is 77 degrees Fahrenheit.
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https://brainly.com/question/1462499
this isn't a test I'm just trying to make up some missing work and this one really confuses me if you guys could explain it the question is in the screenshot I linked to this question
Answer:
They are saying that they have this conference room mapped out on a poster board kinda like a road map. But if you put something that big on a board it wont fit. So they had to make it small enough to fit it. When they say that 1/2 on the board is equal to 12 feet in the real room, They are tell you the scale you have to go by. So then they give you 3 1/2 inches on the board. You would see how many 1/2 inches there are in 3 1/2, which is 7, and multiply 7 by 12. The answer would be 84 feet. So they are say that 3 1/2 inches on the poster board, represents 84 feet in the real room.
Step-by-step explanation:
Joy bought b boxes of granola bars. There are 10 granola bars in each box. Write an expression that shows how many granola bars Joy bought.
Answer:
Step-by-step explanation:
i think it might be total granola bars = b(10)
Answer:
The answer is 10b
Step-by-step explanation:
The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (,) and (,) to find the number of soda bottles the machine can make each minute. Number of Soda Bottles Made 0 2 4 6 8 10 0 100 200 300 400 500 Time (minutes) Number of Soda Bottles A coordinate plane titled Number of Soda Bottles Made is shown. A horizontal axis is labeled Time (minutes) from 0 to 10. A vertical axis is labeled Number of Soda Bottles from 0 to 500. A line rises from left to right starting at the origin, (0, 0), and passes through plotted points (4, 200) and (8, 400). The machine can make nothing soda bottles each minute.
Answer: The machine can make 50 soda bottles each minute
You may determine the slope of the line by determining the rise and the run using two of the line's points.
What is Slope of the line?A line's slope is the change in y coordinate in relation to the change in x coordinate. The net change in y-coordinate is denoted by y, while the net change in x-coordinate is denoted by x. Where "m" represents the slope of a line. As a result, tan represents the slope of a line. Calculate the difference in y-coordinates between these two points (rise). Determine the x-coordinate difference between these two points (run). Divide the y-coordinate difference by the x-coordinate difference (rise/run or slope). The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).Therefore,
You may determine the slope of the line by determining the rise and the run using two of the line's points. The rise and the run are terms used to describe changes in height between two points. Rise divided by Run gives you the slope. Run = rise + slope Rise + run = slope.
Variety of Slope:
Undefined visual description: vertical
Unfavourable : downhill
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Is 4.88 x 4.57 x 2.52 inches larger than 4.06 x 1.3 x 3.23 inches?
I think it is but I just want clarification.
Answer:
4.88 x 4.57 x 2.52= 56.200032
4.06 x 1.3 x 3.23= 17.04794
Step-by-step explanation:
Yes 4.88 x 4.57 x 2.52 is larger than 4.06 x 1.3 x 3.23
Which expressions have a positive product? Select all that apply.
A
(-5)(4)(-2)
B
-(-5)(-2)
C
(5)(-4)(2)(-5)
D
(4)(-2)
E
-(-5)(4)(-2)(-5)
Answer:
A:=40
C:=200
E:=200
Step-by-step explanation: